File size: 7,909 Bytes
1fd0050 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 | #include <bits/stdc++.h>
using namespace std;
static const long long P = 998244353;
// Fast evaluator for the generalized chain structure
// n instructions: POP[0]..POP[d-1], HALT[d] where d=n-1
// POP[i]: POP (i+1) GOTO (i+1) PUSH push_val[i] GOTO push_goto[i]
// HALT: HALT PUSH halt_push GOTO halt_goto
//
// Constraint for no cycles: push_goto[i] <= i (goes to same or earlier instruction)
// This ensures the recursion terminates because:
// - solve(i, v) for v != i+1 calls solve(push_goto[i], push_val[i]) where push_goto[i] <= i
// This resolves to some instruction j <= i with some value x
// Then calls solve(j, v)
// Since j <= i and the chain makes progress, this terminates
//
// Actually, we need to be more careful. Let me use the standard chain constraint
// and just vary push_val.
// With the standard chain (push_goto[i] goes to some j <= i, pop_goto=i+1):
// The recursion for solve(i, x) where x != i+1:
// First: solve(push_goto[i], push_val[i])
// This pushes push_val[i] at instruction push_goto[i]
// If push_val[i] == push_goto[i]+1, it matches immediately -> (push_goto[i]+1, 1)
// If push_val[i] != push_goto[i]+1, it recurses deeper
// Then: solve(result, x) processes x at the resulting instruction
//
// The key insight: if push_val[i] != i+1 (not the standard value),
// the behavior changes because the pushed value may or may not match at the target instruction.
// Let me compute the cost using iterative DP
// States: (instruction, value) where value in {0, 1, ..., maxVal}
// We process in topological order
struct State {
int instr;
int val;
};
int main() {
long long targets[2] = {150994941LL, 150994939LL};
for (int n = 8; n <= 27; n++) {
int d = n - 1;
// Allow push values 1..d (same as pop values)
// push_goto[i] in 0..i (goes to same or earlier)
// halt_push in 1..d, halt_goto in 0..d-1
cerr << "n=" << n << " d=" << d << endl;
mt19937 rng(42 + n * 7777);
bool found[2] = {false, false};
auto startTime = chrono::steady_clock::now();
int timeLimit = (n <= 15) ? 15000 : (n <= 20) ? 10000 : 5000;
long long total_attempts = 0;
while (!(found[0] && found[1])) {
auto now = chrono::steady_clock::now();
auto ms = chrono::duration_cast<chrono::milliseconds>(now - startTime).count();
if (ms > timeLimit) break;
// Random config
int push_val[30], push_goto[30];
int halt_push, halt_goto;
for (int i = 0; i < d; i++) {
push_val[i] = 1 + rng() % d; // 1..d
push_goto[i] = rng() % (i + 1); // 0..i
}
halt_push = 1 + rng() % d;
halt_goto = rng() % d;
// Evaluate using recursive DP with cycle detection
// States: (instr 0..d, val 0..d)
// val 0 = empty stack
int maxVal = d;
int nstates = (d + 1) * (maxVal + 1);
vector<int> dest(nstates, -2);
vector<long long> cost(nstates, 0);
vector<int8_t> st(nstates, 0); // 0=unvisited, 1=in-progress, 2=done
bool cycle = false;
function<pair<int,long long>(int,int)> solve = [&](int i, int x) -> pair<int,long long> {
int id = i * (maxVal + 1) + x;
if (st[id] == 2) return {dest[id], cost[id]};
if (st[id] == 1) { cycle = true; return {-2, 0}; }
st[id] = 1;
int dd; long long cc;
if (i < d) { // POP
int pv = i + 1; // pop_val
if (x == pv) {
dd = i + 1; cc = 1; // pop, goto next
} else {
auto [j, u] = solve(push_goto[i], push_val[i]);
if (cycle) return {-2, 0};
if (j < 0 || j > d) { cycle = true; return {-2, 0}; }
auto [k, v] = solve(j, x);
if (cycle) return {-2, 0};
dd = k; cc = (u + v + 1) % P;
}
} else { // HALT (i == d)
if (x == 0) {
dd = -1; cc = 1;
} else {
auto [j, u] = solve(halt_goto, halt_push);
if (cycle) return {-2, 0};
if (j < 0 || j > d) { cycle = true; return {-2, 0}; }
auto [k, v] = solve(j, x);
if (cycle) return {-2, 0};
dd = k; cc = (u + v + 1) % P;
}
}
st[id] = 2; dest[id] = dd; cost[id] = cc;
return {dd, cc};
};
auto [_, T] = solve(0, 0);
total_attempts++;
if (cycle) continue;
// Hill climbing
for (int iter = 0; iter < 30000; iter++) {
for (int ti = 0; ti < 2; ti++) {
if (!found[ti] && T == targets[ti]) {
found[ti] = true;
cerr << "FOUND n=" << n << " target" << (ti+1) << " T=" << T << endl;
cout << "TARGET" << (ti+1) << " n=" << n << endl;
cout << n << endl;
for (int i = 0; i < d; i++) {
cout << "POP " << (i+1) << " GOTO " << (i+2)
<< " PUSH " << push_val[i] << " GOTO " << (push_goto[i]+1) << endl;
}
cout << "HALT PUSH " << halt_push << " GOTO " << (halt_goto+1) << endl;
}
}
if (found[0] && found[1]) break;
// Mutate
int save_pv, save_pg, save_idx, save_hp, save_hg;
int mut = rng() % 3;
if (mut == 0 && d > 0) {
save_idx = rng() % d;
save_pv = push_val[save_idx];
push_val[save_idx] = 1 + rng() % d;
} else if (mut == 1 && d > 0) {
save_idx = rng() % d;
save_pg = push_goto[save_idx];
push_goto[save_idx] = rng() % (save_idx + 1);
} else {
save_hp = halt_push; save_hg = halt_goto;
halt_push = 1 + rng() % d;
halt_goto = rng() % d;
mut = 2;
}
// Re-evaluate
fill(st.begin(), st.end(), (int8_t)0);
cycle = false;
auto [_d, nT] = solve(0, 0);
total_attempts++;
bool accept = false;
if (!cycle) {
long long bestOld = P, bestNew = P;
for (int ti = 0; ti < 2; ti++) {
if (!found[ti]) {
bestOld = min(bestOld, min((T - targets[ti] + P) % P, (targets[ti] - T + P) % P));
bestNew = min(bestNew, min((nT - targets[ti] + P) % P, (targets[ti] - nT + P) % P));
}
}
accept = (bestNew <= bestOld);
}
if (accept) {
T = nT;
} else {
if (mut == 0) push_val[save_idx] = save_pv;
else if (mut == 1) push_goto[save_idx] = save_pg;
else { halt_push = save_hp; halt_goto = save_hg; }
}
}
}
auto ms = chrono::duration_cast<chrono::milliseconds>(chrono::steady_clock::now() - startTime).count();
cerr << " attempts=" << total_attempts << " time=" << ms << "ms found=" << found[0] << "," << found[1] << endl;
if (found[0] && found[1]) break;
}
return 0;
}
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